%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/


%% Created for Robert Fitzpatrick at 2013-04-04 22:52:53 +0800 


%% Saved with string encoding Unicode (UTF-8) 


@inproceedings{DBLP:conf/crypto/DucasDLL13,
  author    = {L{\'e}o Ducas and
               Alain Durmus and
               Tancr{\`e}de Lepoint and
               Vadim Lyubashevsky},
  title     = {Lattice Signatures and Bimodal Gaussians},
  booktitle = {CRYPTO (1)},
  year      = {2013},
  pages     = {40-56},
  ee        = {http://dx.doi.org/10.1007/978-3-642-40041-4_3},
  crossref  = {DBLP:conf/crypto/2013-1},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}

@proceedings{DBLP:conf/crypto/2013-1,
  editor    = {Ran Canetti and
               Juan A. Garay},
  title     = {Advances in Cryptology - CRYPTO 2013 - 33rd Annual Cryptology
               Conference, Santa Barbara, CA, USA, August 18-22, 2013.
               Proceedings, Part I},
  booktitle = {CRYPTO (1)},
  publisher = {Springer},
  series    = {Lecture Notes in Computer Science},
  volume    = {8042},
  year      = {2013},
  isbn      = {978-3-642-40040-7},
  ee        = {http://dx.doi.org/10.1007/978-3-642-40041-4},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}


@inproceedings{SCC12_AG,
  teams = {POLSYS},
  labs = {LIP6},
  author = {Albrecht, Martin and Cid, Carlos and  Faugère, Jean-Charles and  Fitzpatrick, Robert and Perret, Ludovic},
  title = {On the Complexity of the Arora-Ge algorithm against LWE},
  booktitle = {SCC '12: Proceedings of the 3nd International Conference on Symbolic Computation and Cryptography},
  pages = {93--99},
  year = {2012},
  address = {Castro-Urdiales},
  location = {Castro-Urdiales (Spain)},
  month = {July},
  x-proceedings = {yes},
  x-editorial-board = {yes},
  x-international-audience = {yes}
}


@misc{cryptoeprint:2013:630,
    author = {Joop van de Pol and Nigel P. Smart},
    title = {Estimating Key Sizes For High Dimensional Lattice Based Systems},
    howpublished = {Cryptology ePrint Archive, Report 2013/630},
    year = {2013},
    note = {\url{http://eprint.iacr.org/}},
}


@inproceedings{DBLP:conf/tcc/Pietrzak12,
	Author = {Krzysztof Pietrzak},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {TCC},
	Crossref = {DBLP:conf/tcc/2012},
	Ee = {http://dx.doi.org/10.1007/978-3-642-28914-9_31},
	Pages = {548-563},
	Title = {Subspace {LWE}},
	Year = {2012}}

@proceedings{DBLP:conf/tcc/2012,
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {TCC},
	Editor = {Ronald Cramer},
	Ee = {http://dx.doi.org/10.1007/978-3-642-28914-9},
	Isbn = {978-3-642-28913-2},
	Publisher = {Springer},
	Series = {Lecture Notes in Computer Science},
	Title = {Theory of Cryptography - 9th Theory of Cryptography Conference, TCC 2012, Taormina, Sicily, Italy, March 19-21, 2012. Proceedings},
	Volume = {7194},
	Year = {2012}}

@proceedings{DBLP:conf/tcc/2009,
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {TCC},
	Editor = {Omer Reingold},
	Ee = {http://dx.doi.org/10.1007/978-3-642-00457-5},
	Isbn = {978-3-642-00456-8},
	Publisher = {Springer},
	Series = {Lecture Notes in Computer Science},
	Title = {Theory of Cryptography, 6th Theory of Cryptography Conference, TCC 2009, San Francisco, CA, USA, March 15-17, 2009. Proceedings},
	Volume = {5444},
	Year = {2009}}

@inproceedings{DBLP:conf/innovations/GoldwasserKPV10,
	Author = {Shafi Goldwasser and Yael Tauman Kalai and Chris Peikert and Vinod Vaikuntanathan},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {ICS},
	Crossref = {DBLP:conf/innovations/2010},
	Ee = {http://conference.itcs.tsinghua.edu.cn/ICS2010/content/papers/19.html},
	Pages = {230-240},
	Title = {Robustness of the {L}earning with {E}rrors Assumption},
	Year = {2010}}

@proceedings{DBLP:conf/innovations/2010,
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {ICS},
	Editor = {Andrew Chi-Chih Yao},
	Isbn = {978-7-302-21752-7},
	Publisher = {Tsinghua University Press},
	Title = {Innovations in Computer Science - ICS 2010, Tsinghua University, Beijing, China, January 5-7, 2010. Proceedings},
	Year = {2010}}

@inproceedings{DBLP:conf/crypto/DuboisFSS07,
	Author = {Vivien Dubois and Pierre-Alain Fouque and Adi Shamir and Jacques Stern},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {CRYPTO},
	Crossref = {DBLP:conf/crypto/2007},
	Ee = {http://dx.doi.org/10.1007/978-3-540-74143-5_1},
	Pages = {1-12},
	Title = {Practical Cryptanalysis of SFLASH},
	Year = {2007}}

@proceedings{DBLP:conf/crypto/2007,
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {CRYPTO},
	Editor = {Alfred Menezes},
	Isbn = {978-3-540-74142-8},
	Publisher = {Springer},
	Series = {Lecture Notes in Computer Science},
	Title = {Advances in Cryptology - CRYPTO 2007, 27th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 19-23, 2007, Proceedings},
	Volume = {4622},
	Year = {2007}}

@inproceedings{DBLP:conf/acisp/YangC05,
	Author = {Bo-Yin Yang and Jiun-Ming Chen},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {ACISP},
	Crossref = {DBLP:conf/acisp/2005},
	Ee = {http://dx.doi.org/10.1007/11506157_43},
	Pages = {518-531},
	Title = {Building Secure Tame-like Multivariate Public-Key Cryptosystems: The New TTS},
	Year = {2005}}

@proceedings{DBLP:conf/acisp/2005,
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {ACISP},
	Editor = {Colin Boyd and Juan Manuel Gonz{\'a}lez Nieto},
	Isbn = {3-540-26547-3},
	Publisher = {Springer},
	Series = {Lecture Notes in Computer Science},
	Title = {Information Security and Privacy, 10th Australasian Conference, ACISP 2005, Brisbane, Australia, July 4-6, 2005, Proceedings},
	Volume = {3574},
	Year = {2005}}

@inproceedings{KS99,
	Author = {Aviad Kipnis and Adi Shamir},
	Booktitle = {Advances in Cryptology -- CRYPTO '99},
	Pages = {19--30},
	Publisher = {Springer},
	Series = {LNCS},
	Title = {Cryptanalysis of the {HFE} {Public Key Cryptosystem} by {Relinearization}},
	Volume = 1666,
	Year = 1999}

@inproceedings{CG00,
	Author = {Nicolas Courtois and Louis Goubin},
	Booktitle = {Advances in Cryptology -- ASIACRYPT '00},
	Pages = {44--57},
	Publisher = {Springer},
	Series = {Lecture Notes in Computer Science},
	Title = {Cryptanalysis of the {TTM} Cryptosystem},
	Volume = 1976,
	Year = 2000}

@inproceedings{FP06a,
	Author = {Faug{\`e}re, Jean-Charles and Perret, Ludovic},
	Booktitle = {Advances in Cryptology - CRYPTO 2006},
	Editor = {Dwork, Cynthia},
	Location = {Santa Barbara, USA},
	Month = {August},
	Pages = {357-372},
	Publisher = {Springer Berlin / Heidelberg},
	Series = {Lecture Notes in Computer Science},
	Title = {{Cryptanalysis of 2R-- Schemes}},
	Url = {http://www-salsa.lip6.fr/~jcf/Papers/FP06a.pdf},
	Volume = {4117},
	Year = {2006},
	Bdsk-Url-1 = {http://www-salsa.lip6.fr/~jcf/Papers/FP06a.pdf}}

@book{BCC,
	Address = {Berlin, Heidelberg, New York},
	Author = {Sala, M. and Mora, T. and Perret, L. and Sakata, S. and Traverso, C.},
	Pages = {1--430},
	Publisher = {Springer},
	Title = {Gr{\"o}bner Bases, Coding, and Cryptography},
	Year = {2009}}

@book{Kob98,
	Author = {Neal Koblitz},
	Publisher = {{Springer-Verlag}},
	Series = {{Algorithms and Computation in Mathematics}},
	Title = {{Algebraic Aspects of Cryptography.}},
	Volume = 3,
	Year = 1998}

@book{DBLP:books/daglib/0014704,
	Author = {Christopher Wolf},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Isbn = {978-9-05-682649-9},
	Pages = {I-XXIV, 1-155},
	Publisher = {Univ. Leuven Heverlee},
	Title = {Multivariate quadratic polynomials in public key cryptography},
	Year = {2005}}

@incollection{BilletDingSurvey,
	Address = {Berlin, Heidelberg, New York},
	Author = {Olivier Billet and Jintai Ding},
	Booktitle = {Gr\"obner Bases. Coding and Cryptography},
	Editor = {Massimiliano Sala and Teo Mora and Ludovic Perret and Shojiro Sakata and Carlo Traverso},
	Pages = {285-305},
	Publisher = {Springer Verlag},
	Title = {Overview of Cryptanalysis Techniques in Multivariate Public Key Cryptography},
	Year = {2009}}

@incollection{DingYangSurvey,
	Address = {Berlin, Heidelberg, New York},
	Author = {Jintai Ding and Bo-Yin Yang},
	Booktitle = {Post-Quantum Cryptography},
	Editor = {Bernstein, Daniel J. and Buchmann, Johannes and Dahmen, Erik},
	Pages = {193-234},
	Publisher = {Springer Verlag},
	Title = {Multivariate Public Key Cryptography},
	Year = {2009}}

@inproceedings{Cstar,
	Author = {Tsutomu Matsumoto and Hideki Imai},
	Booktitle = {Advances in Cryptology -- EUROCRYPT 1988},
	Pages = {419--453},
	Publisher = {Springer--Verlag},
	Series = {LNCS},
	Title = {Public Quadratic Polynomial-tuples for Efficient Signature-Verification and Message-Encryption},
	Volume = 330,
	Year = 1988}

@inproceedings{SFLASH,
	Author = {Jacques Patarin and Louis Goubin and Nicolas Courtois},
	Booktitle = {Advances in Cryptology - Asiacrypt'98},
	Pages = {35-49},
	Publisher = {Springer},
	Title = {C$^*-+$ and HM: Variations Around Two Schemes of T.Matsumoto and H.Imai},
	Volume = 1514,
	Year = 1998}

@inproceedings{Pat96,
	Author = {Jacques Patarin},
	Booktitle = {Advances in Cryptology -- EUROCRYPT '96},
	Pages = {33--48},
	Publisher = {Springer},
	Series = {Lecture Notes in Computer Science},
	Title = {{Hidden Fields Equations (HFE)} and {Isomorphisms of Polynomials (IP)}: two new families of asymmetric algorithms},
	Volume = 1070,
	Year = 1996}

@inproceedings{KPG99,
	Author = {Aviad Kipnis and Jacques Patarin and Louis Goubin},
	Booktitle = {Advances in Cryptology -- EUROCRYPT '99},
	Pages = {206--222},
	Publisher = {Springer},
	Series = {Lecture Notes in Computer Science},
	Title = {Unbalanced Oil and Vinegar Signature Schemes},
	Volume = 1592,
	Year = 1999}

@inproceedings{QUARTZ,
	Author = {Jacques Patarin and Nicolas Courtois and Louis Goubin},
	Booktitle = {CT-RSA'01},
	Pages = {282-297},
	Publisher = {Springer},
	Title = {QUARTZ, 128-Bit Long Digital Signatures},
	Volume = 2020,
	Year = 2001}

@book{DBLP:books/daglib/0010544,
	Author = {Joachim von zur Gathen and J{\"u}rgen Gerhard},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Isbn = {978-0-521-82646-4},
	Pages = {I-XIII, 1-785},
	Publisher = {Cambridge University Press},
	Title = {Modern computer algebra (2. ed.)},
	Year = {2003}}

@inproceedings{DBLP:conf/stoc/Williams12,
	Author = {Virginia Vassilevska Williams},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {STOC},
	Crossref = {DBLP:conf/stoc/2012},
	Ee = {http://doi.acm.org/10.1145/2213977.2214056},
	Pages = {887-898},
	Title = {Multiplying matrices faster than {C}oppersmith-{W}inograd},
	Year = {2012}}

@proceedings{DBLP:conf/stoc/2012,
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {STOC},
	Editor = {Howard J. Karloff and Toniann Pitassi},
	Ee = {http://dl.acm.org/citation.cfm?id=2213977},
	Isbn = {978-1-4503-1245-5},
	Publisher = {ACM},
	Title = {Proceedings of the 44th Symposium on Theory of Computing Conference, STOC 2012, New York, NY, USA, May 19 - 22, 2012},
	Year = {2012}}

@phdthesis{sto:thesis2010,
	Author = {A. J. Stothers},
	School = {University of Edinburgh},
	Title = {On the Complexity of Matrix Multiplication},
	Year = {2010}}

@article{DBLP:journals/jsc/BerbainGP09,
	Author = {C{\^o}me Berbain and Henri Gilbert and Jacques Patarin},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Ee = {http://dx.doi.org/10.1016/j.jsc.2008.10.004},
	Journal = {J. Symb. Comput.},
	Number = {12},
	Pages = {1703-1723},
	Title = {{QUAD}: A multivariate stream cipher with provable security},
	Volume = {44},
	Year = {2009}}

@inproceedings{DBLP:conf/vietcrypt/GougetP06,
	Author = {Aline Gouget and Jacques Patarin},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Crossref = {DBLP:conf/vietcrypt/2006},
	Ee = {http://dx.doi.org/10.1007/11958239_1},
	Pages = {1-18},
	Title = {Probabilistic Multivariate Cryptography},
	Year = {2006}}

@proceedings{DBLP:conf/vietcrypt/2006,
	Address = {Berlin, Heidelberg, New York},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {Progress in Cryptology - VIETCRYPT 2006},
	Editor = {Phong Q. Nguyen},
	Isbn = {3-540-68799-8},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Volume = {4341},
	Year = {2006}}

@inproceedings{brakerski-langlois-peikert-regev-stehle:stoc13,
	author = {Zvika Brakerski and Adeline Langlois and Chris Peikert and Oded Regev and Damien Stehl{\'e}},
    booktitle = {STOC '13},
    pages = {575-584},
    publisher = {ACM},
    address = {New York},
	title = {Classical Hardness of {L}earning with {E}rrors},
	year = 2013
}

@inproceedings{micciancio-peikert:crypto2013,
    title = {Hardness of {SIS} and {LWE} with Small Parameters},
    author = {Daniele Micciancio and Chris Peikert},
    booktitle = {Advances in Cryptology -- CRYPTO 2013},
    editor = {Ran Canetti and Juan Garay},
    publisher = {Springer Verlag},
    series = {Lecture Notes in Computer Science},
    year = 2013,
    note = {to appear, pre-print available as Cryptology ePrint Archive, Report 2013/069, \url{http://eprint.iacr.org/2013/069}}
}

@inproceedings{F5,
	Address = {New York},
	Author = {Jean-Charles Faug{\`e}re},
	Booktitle = {Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation},
	File = {:http\://www-spaces.lip6.fr/%40papers/F02a.pdf:PDF},
	Owner = {malb},
	Pages = {75-83},
	Publisher = {ACM},
	Timestamp = {2008.02.19},
	Title = {A New Efficient Algorithm for Computing {G}r{\"o}bner Bases without Reduction to Zero ({F5})},
	Year = {2002}}

@article{F4,
	Author = {Jean-Charles Faug{\`e}re},
	Eid = {10.1016/S0022-4049(99)00005-5},
	File = {:Algebraic Attacks/F4.pdf:PDF;:http\://modular.ucsd.edu/129-05/refs/faugere_f4.pdf:PDF},
	Journal = {Journal of Pure and Applied Algebra},
	Number = {1-3},
	Owner = {malb},
	Pages = {61-88},
	Timestamp = {2008.02.19},
	Title = {A New Efficient Algorithm for Computing {G}r{\"o}bner Basis ({F4})},
	Volume = {139},
	Year = {1999}}

@phdthesis{bardet:thesis2004,
	Author = {Magali Bardet},
	School = {Universit\'e Paris VI},
	Title = {\'Etude des syst\`emes alg\'ebriques surd\'etermin\'es. Applications aux codes correcteurs et \`a la cryptographie},
	Year = {2004}}

@techreport{bardet-faugere-salvy:tech,
	Author = {Magali Bardet and Jean-Charles Faug\`ere and Bruno Salvy},
	Institution = {INRIA},
	Month = {December},
	Note = {Available at \url{http://www.inria.fr/rrrt/rr-5049.html}},
	Number = {5049},
	Title = {Complexity of {G}r\"obner basis computation for semi-regular overdetermined sequences over {$F_2$} with solutions in {$F_2$}},
	Year = {2003}}

@inproceedings{BFS05,
	Author = {Bardet, Magali and Faug{\`e}re, Jean-Charles and Salvy, Bruno},
	Booktitle = {The Effective Methods in Algebraic Geometry Conference, Mega 2005},
	Editor = {P. Gianni},
	Location = {Porto Conte, Sardinia, Italy},
	Month = {May},
	Pages = {1 -14},
	Title = {Asymptotic Expansion of the Degree of Regularity for Semi-Regular Systems of Equations},
	Url = {http://www-salsa.lip6.fr/~jcf/Papers/BFS05.pdf},
	Year = 2005,
	Bdsk-Url-1 = {http://www-salsa.lip6.fr/~jcf/Papers/BFS05.pdf}}

@book{Becker1991,
	Address = {Berlin, Heidelberg, New York},
	Author = {Thomas Becker and Volker Weispfenning},
	File = {:/home/malb/Desktop/eBooks/Math eBooks/Becker, Weispfenning -- Groebner Bases.djvu:Djvu},
	Owner = {malb},
	Publisher = {Springer Verlag},
	Timestamp = {2008.02.19},
	Title = {{Gr{\"o}bner Bases - A Computational Approach to Commutative Algebra}},
	Year = {1991}}

@article{albrecht-cid-faugere-fitzpatrick-perret:dcc2013,
	Author = {Martin R.\ Albrecht and Carlos Cid and Jean-Charles Faug{\`e}re and Robert Fitzpatrick and Ludovic Perret},
	journal = {Designs, Codes and Cryptography},
	title = {On the Complexity of the {BKW} Algorithm on {LWE}},
    doi = {10.1007/s10623-013-9864-x},
	year = 2013,
    issn={0925-1022},
    url={http://dx.doi.org/10.1007/s10623-013-9864-x},
    publisher={Springer Verlag},
    pages={1-30},
}

@article{DBLP:journals/iacr/PujolS09,
	Author = {Xavier Pujol and Damien Stehl{\'e}},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Ee = {http://eprint.iacr.org/2009/605},
	Journal = {IACR Cryptology ePrint Archive},
	Pages = {605},
	Title = {Solving the Shortest Lattice Vector Problem in Time $2^{2.465n}$},
	Volume = {2009},
	Year = {2009}}

@inproceedings{DBLP:conf/issac/MorelSV09,
	Author = {Ivan Morel and Damien Stehl{\'e} and Gilles Villard},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {Symbolic and Algebraic Computation, International Symposium, ISSAC 2009},
	Crossref = {DBLP:conf/issac/2009},
	Ee = {http://doi.acm.org/10.1145/1576702.1576740},
	Pages = {271-278},
	Title = {{H-LLL}: using householder inside {LLL}},
	Year = {2009}}

@proceedings{DBLP:conf/issac/2009,
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {Symbolic and Algebraic Computation, International Symposium, ISSAC 2009},
	Editor = {Jeremy R. Johnson and Hyungju Park and Erich Kaltofen},
	Isbn = {978-1-60558-609-0},
	Publisher = {ACM},
	Year = {2009}}

@inproceedings{hanrot-pujol-stehle:crypto2011,
	Author = {Guillaume Hanrot and Xavier Pujol and Damien Stehl{\'e}},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {Advances in Cryptology -- CRYPTO 2011},
	Editor = {Phillip Rogaway},
	Ee = {http://dx.doi.org/10.1007/978-3-642-22792-9_25},
	Pages = {447-464},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {Analyzing Blockwise Lattice Algorithms Using Dynamical Systems},
	Volume = {6841},
	Year = {2011}}

@article{nguyen-stehle:talgs2009,
	Author = {Phong Q. Nguyen and Damien Stehl{\'e}},
	Ee = {http://doi.acm.org/10.1145/1597036.1597050},
	Journal = {ACM Transactions on Algorithms},
	Number = {4},
	Title = {Low-dimensional lattice basis reduction revisited},
	Volume = {5},
	Year = {2009}}

@inproceedings{gama-nguyen-regev:eurocrypt2010,
	Author = {Nicolas Gama and Phong Q. Nguyen and Oded Regev},
	Booktitle = {Advances in Cryptology -- EUROCRYPT 2010},
	Ee = {http://dx.doi.org/10.1007/978-3-642-13190-5_13},
	Pages = {257-278},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {Lattice Enumeration Using Extreme Pruning},
	Volume = {6110},
	Year = {2010}}

@inproceedings{nguyen:eurocrypt2011,
	Author = {Phong Q. Nguyen},
	Booktitle = {Advances in Cryptology - EUROCRYPT 2011},
	Editor = {Kenneth G. Paterson},
	Ee = {http://dx.doi.org/10.1007/978-3-642-20465-4_2},
	Pages = {2-6},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {Lattice Reduction Algorithms: Theory and Practice},
	Volume = {6632},
	Year = {2011}}

@article{BFP09b,
	Address = {Berlin, Newyork},
	Author = {Bettale, Luk and Faug\`ere, Jean-Charles and Perret, Ludovic},
	Doi = {10.1515/JMC.2009.009},
	Issn = {1862-2976},
	Journal = {Journal of Mathematical Cryptology},
	Number = {3},
	Pages = {177--197},
	Publisher = {De Gruter},
	Title = {{H}ybrid {A}pproach for solving multivariate systems over finite fields},
	Url = {http://www-salsa.lip6.fr/~jcf/Papers/JMC2.pdf},
	Volume = {3},
	X-Editorial-Board = {yes},
	X-International-Audience = {yes},
	Year = {2010},
	Bdsk-Url-1 = {http://www-salsa.lip6.fr/~jcf/Papers/JMC2.pdf},
	Bdsk-Url-2 = {http://dx.doi.org/10.1515/JMC.2009.009}}

@inproceedings{FBP12,
	Address = {New York, NY, USA},
	Author = {Bettale, Luk and Faug\`ere, Jean-Charles and Perret, Ludovic},
	Booktitle = {ISSAC '12: Proceedings of the 2012 international symposium on Symbolic and algebraic computation},
	Lip6-Rank = {A},
	Location = {Grenoble, France},
	Pages = {1--12},
	Publisher = {ACM},
	Series = {ISSAC '12},
	Title = {Solving polynomial systems over Finite Fields: Improved Analysis of the {H}ybrid {A}pproach},
	Url = {http://www-salsa.lip6.fr/~jcf/Papers/FBP12.pdf},
	Year = {2012},
	Bdsk-Url-1 = {http://www-salsa.lip6.fr/~jcf/Papers/FBP12.pdf}}

@inproceedings{howgrave-graham-joux:eurocrypt2010,
	Author = {Nick Howgrave-Graham and Antoine Joux},
	Booktitle = {Advances in Cryptology - EUROCRYPT 2010},
	Editor = {Henri Gilbert},
	Ee = {http://dx.doi.org/10.1007/978-3-642-13190-5_12},
	Pages = {235-256},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {New Generic Algorithms for Hard {K}napsacks},
	Volume = {6110},
	Year = {2010}}

@inproceedings{becker-coron-joux:eurocrypt2011,
	Author = {Anja Becker and Jean-S{\'e}bastien Coron and Antoine Joux},
	Booktitle = {Advances in Cryptology - EUROCRYPT 2011},
	Editor = {Kenneth G. Paterson},
	Ee = {http://dx.doi.org/10.1007/978-3-642-20465-4_21},
	Pages = {364-385},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {Improved Generic Algorithms for Hard {K}napsacks},
	Volume = {6632},
	Year = {2011}}

@inproceedings{DBLP:conf/asiacrypt/FiniaszS09,
	Author = {Matthieu Finiasz and Nicolas Sendrier},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {ASIACRYPT},
	Crossref = {DBLP:conf/asiacrypt/2009},
	Ee = {http://dx.doi.org/10.1007/978-3-642-10366-7_6},
	Pages = {88-105},
	Title = {Security Bounds for the Design of Code-Based Cryptosystems},
	Year = {2009}}

@inproceedings{DBLP:conf/eurocrypt/BeckerJMM12,
	Author = {Anja Becker and Antoine Joux and Alexander May and Alexander Meurer},
	Booktitle = {Advances in Cryptology - EUROCRYPT 2012},
	Editor = {David Pointcheval and Thomas Johansson},
	Ee = {http://dx.doi.org/10.1007/978-3-642-29011-4_31},
	Pages = {520-536},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {Decoding Random Binary Linear Codes in $2^{n/20}$: How $1 + 1 = 0$ Improves {Information Set Decoding}},
	Volume = {7237},
	Year = {2012}}

@inproceedings{DBLP:conf/asiacrypt/MayMT11,
	Author = {Alexander May and Alexander Meurer and Enrico Thomae},
	Booktitle = {Advances in Cryptology - ASIACRYPT 2011},
	Editor = {Dong Hoon Lee and Xiaoyun Wang},
	Ee = {http://dx.doi.org/10.1007/978-3-642-25385-0},
	Pages = {107-124},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {Decoding Random Linear Codes in $\tilde{O}(2^{0.054n})$},
	Volume = {7073},
	Year = {2011}}

@inproceedings{bernstein-lange-peters:crypto2011,
	Author = {Daniel J. Bernstein and Tanja Lange and Christiane Peters},
	Booktitle = {Advances in Cryptology - CRYPTO 2011},
	Editor = {Phillip Rogaway},
	Ee = {http://dx.doi.org/10.1007/978-3-642-22792-9_42},
	Pages = {743-760},
	Publisher = {Springer Verlag},
	Title = {Smaller Decoding Exponents: Ball-Collision Decoding},
	Volume = {6841},
	Year = {2011}}

@inproceedings{DBLP:conf/pqcrypto/BernsteinLP08,
	Author = {Daniel J. Bernstein and Tanja Lange and Christiane Peters},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {PQCrypto},
	Crossref = {DBLP:conf/pqcrypto/2008},
	Ee = {http://dx.doi.org/10.1007/978-3-540-88403-3_3},
	Pages = {31-46},
	Title = {Attacking and Defending the {McEliece} Cryptosystem},
	Year = {2008}}

@proceedings{DBLP:conf/pqcrypto/2008,
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {PQCrypto},
	Editor = {Johannes Buchmann and Jintai Ding},
	Isbn = {978-3-540-88402-6},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {Post-Quantum Cryptography, Second International Workshop, PQCrypto 2008, Cincinnati, OH, USA, October 17-19, 2008, Proceedings},
	Volume = {5299},
	Year = {2008}}

@inproceedings{DBLP:conf/ima/AlbrechtP11,
	Author = {Martin R. Albrecht and Kenneth G. Paterson},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {IMA Int. Conf.},
	Crossref = {DBLP:conf/ima/2011},
	Ee = {http://dx.doi.org/10.1007/978-3-642-25516-8_21},
	Pages = {344-355},
	Title = {Breaking an Identity-Based Encryption Scheme Based on DHIES},
	Year = {2011}}

@proceedings{DBLP:conf/ima/2011,
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {IMA Int. Conf.},
	Editor = {Liqun Chen},
	Ee = {http://dx.doi.org/10.1007/978-3-642-25516-8},
	Isbn = {978-3-642-25515-1},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {Cryptography and Coding - 13th IMA International Conference, IMACC 2011, Oxford, UK, December 12-15, 2011. Proceedings},
	Volume = {7089},
	Year = {2011}}

@inproceedings{DBLP:conf/acns/AlbrechtC11,
	Author = {Martin R. Albrecht and Carlos Cid},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {ACNS},
	Crossref = {DBLP:conf/acns/2011},
	Ee = {http://dx.doi.org/10.1007/978-3-642-21554-4_4},
	Pages = {57-72},
	Title = {Cold Boot Key Recovery by Solving Polynomial Systems with Noise},
	Year = {2011}}

@proceedings{DBLP:conf/acns/2011,
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {ACNS},
	Editor = {Javier Lopez and Gene Tsudik},
	Ee = {http://dx.doi.org/10.1007/978-3-642-21554-4},
	Isbn = {978-3-642-21553-7},
	Series = {Lecture Notes in Computer Science},
	Title = {Applied Cryptography and Network Security - 9th International Conference, ACNS 2011, Nerja, Spain, June 7-10, 2011. Proceedings},
	Volume = {6715},
	Year = {2011}}

@inproceedings{DBLP:conf/eurocrypt/FaugerePPR12,
	Author = {Jean-Charles Faug{\`e}re and Ludovic Perret and Christophe Petit and Gu{\'e}na{\"e}l Renault},
	Booktitle = {Advances in Cryptology - EUROCRYPT 2012},
	Editor = {David Pointcheval and Thomas Johansson},
	Ee = {http://dx.doi.org/10.1007/978-3-642-29011-4_4},
	Pages = {27-44},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {Improving the Complexity of Index Calculus Algorithms in Elliptic Curves over Binary Fields},
	Volume = {7237},
	Year = {2012}}

@inproceedings{lazard:eurocal83,
	Address = {Berlin, Heidelberg, New York},
	Author = {Daniel Lazard},
	Booktitle = {Proceedings of the European Computer Algebra Conference on Computer Algebra},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {Gr\"obner-Bases, {G}aussian elimination and resolution of systems of algebraic equations},
	Volume = {162},
	Year = {1983}}

@article{Mac02,
	Author = {Macaulay, Francis S.},
	Journal = {London Mathematical Society},
	Number = 33,
	Pages = {3--27},
	Title = {On Some Formula in Elimination},
	Volume = 1,
	Year = 1902}

@inproceedings{arora-ge:icalp2011,
	Author = {Sanjeev Arora and Rong Ge},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {ICALP},
	Crossref = {DBLP:conf/icalp/2011-1},
	Ee = {http://dx.doi.org/10.1007/978-3-642-22006-7_34},
	Pages = {403-415},
	Title = {New Algorithms for Learning in Presence of Errors},
	Year = {2011}}

@proceedings{DBLP:conf/icalp/2011-1,
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {ICALP (1)},
	Editor = {Luca Aceto and Monika Henzinger and Jiri Sgall},
	Ee = {http://dx.doi.org/10.1007/978-3-642-22006-7},
	Isbn = {978-3-642-22005-0},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Zurich, Switzerland, July 4-8, 2011, Proceedings, Part I},
	Volume = {6755},
	Year = {2011}}

@article{BJV04,
	Author = {Thomas Baigneres and Pascal Junod and Serge Vaudenay},
	Date-Added = {2012-05-07 19:52:51 +0100},
	Date-Modified = {2012-05-07 19:57:10 +0100},
	Journal = {Advances in Cryptology - Asiacrypt 2004},
	Title = {How Far Can We Go Beyond Linear Cryptanalysis?},
	Year = {2004}}

@article{BVCDD,
	Author = {Thomas Baigneres and Serge Vaudenay},
	Date-Added = {2012-05-05 18:25:56 +0100},
	Date-Modified = {2012-05-05 18:40:08 +0100},
	Title = {The Complexity of Distinguishing Distributions},
	Year = {2008}}

@book{Joux2100,
	Author = {Antoine Joux},
	Publisher = {{Chapman \& Hall}},
	Series = {{CRC Cryptography and Network Security Series}},
	Title = {{Algorithmic Cryptanalysis}},
	Year = 2009}

@inproceedings{DBLP:conf/eurocal/Lazard83,
	Author = {Daniel Lazard},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {EUROCAL},
	Crossref = {DBLP:conf/eurocal/1983},
	Pages = {146-156},
	Title = {Gr{\"o}bner-Bases, Gaussian elimination and resolution of systems of algebraic equations},
	Year = {1983}}

@proceedings{DBLP:conf/eurocal/1983,
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {EUROCAL},
	Editor = {J. A. van Hulzen},
	Isbn = {3-540-12868-9},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {Computer Algebra, EUROCAL '83, European Computer Algebra Conference, London, England, March 28-30, 1983, Proceedings},
	Volume = {162},
	Year = {1983}}

@misc{Shoup04acomputational,
	Author = {Victor Shoup},
	Title = {A COMPUTATIONAL INTRODUCTION TO NUMBER THEORY AND ALGEBRA},
	Year = {2004}}

@article{para_lattice,
	Author = {Markus R{\"u}ckert and Michael Schneider},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Ee = {http://eprint.iacr.org/2010/137},
	Journal = {Cryptology ePrint Archive},
	Number = {2010/137},
	Title = {Estimating the Security of Lattice-based Cryptosystems},
	Year = {2010}}

@article{DBLP:journals/dcc/Stinson94,
	Author = {Douglas R. Stinson},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Journal = {Des. Codes Cryptography},
	Number = {4},
	Pages = {369-380},
	Title = {Universal Hashing and Authentication Codes},
	Volume = {4},
	Year = {1994}}

@inproceedings{RX,
	Author = {M. Renauld and F.-X. Standaert},
	Booktitle = {Inscrypt},
	Pages = {To appear},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {Algebraic Side-Channel Attacks},
	Year = {2009}}

@inproceedings{ACDFP,
	Author = {Martin Albrecht and Carlos Cid and Thomas Dullien and Jean-Charles Faug\`ere and Ludovic Perret},
	Booktitle = {Inscrypt},
	Pages = {To appear},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {Algebraic Side-Channel Attacks},
	Year = {2009}}

@techreport{BARDET:2003:INRIA-00071534:1,
	Affiliation = {{SPACES} - {INRIA} {L}orraine - {LORIA} - {INRIA} - {CNRS} : {UMR}7503 - {U}niversit{\'e} {H}enri {P}oincar{\'e} - {N}ancy {I} - {U}niversit{\'e} {N}ancy {II} - {I}nstitut {N}ational {P}olytechnique de {L}orraine - {L}aboratoire d'{I}nformatique de {P}aris 6 - {LIP}6 - {CNRS} : {UMR}7606 - {U}niversit{\'e} {P}ierre et {M}arie {C}urie - {P}aris {VI} - {ALGO} - {INRIA} {R}ocquencourt - {INRIA}},
	Author = {{B}ardet, {M}agali and {F}aug{\`e}re, {J}ean-{C}harles and {S}alvy, {B}runo},
	Hal_Id = {inria-00071534},
	Institution = {INRIA},
	Language = {{A}nglais},
	Number = {{RR}-5049},
	Title = {{C}omplexity of {G}r{\"o}bner basis computation for {S}emi-regular {O}verdetermined sequences over F$_2$ with solutions in F$_2$},
	Type = {Research Report},
	Url = {http://hal.inria.fr/inria-00071534/PDF/RR-5049.pdf},
	Year = {2003},
	Bdsk-Url-1 = {http://hal.inria.fr/inria-00071534/PDF/RR-5049.pdf}}

@inproceedings{DBLP:conf/crypto/FaugereJ03,
	Author = {Jean-Charles Faug{\`e}re and Antoine Joux},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {CRYPTO},
	Crossref = {DBLP:conf/crypto/2003},
	Ee = {http://springerlink.metapress.com/openurl.asp?genre=article{\&}issn=0302-9743{\&}volume=2729{\&}spage=44},
	Pages = {44-60},
	Title = {Algebraic Cryptanalysis of Hidden Field Equation (HFE) Cryptosystems Using Gr{\"o}bner Bases},
	Year = {2003}}

@proceedings{DBLP:conf/crypto/2003,
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {CRYPTO},
	Editor = {Dan Boneh},
	Isbn = {3-540-40674-3},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {Advances in Cryptology - CRYPTO 2003, 23rd Annual International Cryptology Conference, Santa Barbara, California, USA, August 17-21, 2003, Proceedings},
	Volume = {2729},
	Year = {2003}}

@inproceedings{DBLP:conf/tcc/AkaviaGV09,
	Author = {Adi Akavia and Shafi Goldwasser and Vinod Vaikuntanathan},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {TCC},
	Crossref = {DBLP:conf/tcc/2009},
	Ee = {http://dx.doi.org/10.1007/978-3-642-00457-5_28},
	Pages = {474-495},
	Title = {Simultaneous Hardcore Bits and Cryptography against Memory Attacks},
	Year = {2009}}

@proceedings{DBLP:conf/tcc/2009,
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {TCC},
	Editor = {Omer Reingold},
	Ee = {http://dx.doi.org/10.1007/978-3-642-00457-5},
	Isbn = {978-3-642-00456-8},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {Theory of Cryptography, 6th Theory of Cryptography Conference, TCC 2009, San Francisco, CA, USA, March 15-17, 2009. Proceedings},
	Volume = {5444},
	Year = {2009}}

@article{regev:acm09,
	Author = {Oded Regev},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Ee = {http://doi.acm.org/10.1145/1568318.1568324},
	Journal = {J. ACM},
	Number = {6},
	Title = {On lattices, learning with errors, random linear codes, and cryptography},
	Volume = {56},
	Year = {2009}}

@inproceedings{DBLP:conf/crypto/PeikertVW08,
	Author = {Chris Peikert and Vinod Vaikuntanathan and Brent Waters},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {CRYPTO},
	Crossref = {DBLP:conf/crypto/2008},
	Ee = {http://dx.doi.org/10.1007/978-3-540-85174-5_31},
	Pages = {554-571},
	Title = {A Framework for Efficient and Composable Oblivious Transfer},
	Year = {2008}}

@inproceedings{DBLP:conf/crypto/FaugereLP08,
	Author = {Jean-Charles Faug{\`e}re and Fran\c{c}oise Levy-dit-Vehel and Ludovic Perret},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {CRYPTO},
	Crossref = {DBLP:conf/crypto/2008},
	Ee = {http://dx.doi.org/10.1007/978-3-540-85174-5_16},
	Pages = {280-296},
	Title = {Cryptanalysis of MinRank},
	Year = {2008}}

@proceedings{DBLP:conf/crypto/2008,
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {CRYPTO},
	Editor = {David Wagner},
	Isbn = {978-3-540-85173-8},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {Advances in Cryptology - CRYPTO 2008, 28th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 17-21, 2008. Proceedings},
	Volume = {5157},
	Year = {2008}}

@inproceedings{DBLP:conf/ches/OrenKPW10,
	Author = {Yossef Oren and Mario Kirschbaum and Thomas Popp and Avishai Wool},
	Booktitle = {Cryptographic Hardware and Embedded Systems, CHES 2010},
	Editor = {Stefan Mangard and Fran\c{c}ois-Xavier Standaert},
	Ee = {http://dx.doi.org/10.1007/978-3-642-15031-9_29},
	Pages = {428-442},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {Algebraic Side-Channel Analysis in the Presence of Errors},
	Volume = {6225},
	Year = {2010}}

@inproceedings{DBLP:conf/fse/AlbrechtC09,
	Author = {Martin Albrecht and Carlos Cid},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {FSE},
	Crossref = {DBLP:conf/fse/2009},
	Ee = {http://dx.doi.org/10.1007/978-3-642-03317-9_12},
	Pages = {193-208},
	Title = {Algebraic Techniques in Differential Cryptanalysis},
	Year = {2009}}

@proceedings{DBLP:conf/fse/2009,
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {FSE},
	Editor = {Orr Dunkelman},
	Ee = {http://dx.doi.org/10.1007/978-3-642-03317-9},
	Isbn = {978-3-642-03316-2},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {Fast Software Encryption, 16th International Workshop, FSE 2009, Leuven, Belgium, February 22-25, 2009, Revised Selected Papers},
	Volume = {5665},
	Year = {2009}}

@inproceedings{DBLP:conf/ches/RenauldSV09,
	Author = {Mathieu Renauld and Fran\c{c}ois-Xavier Standaert and Nicolas Veyrat-Charvillon},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {CHES},
	Crossref = {DBLP:conf/ches/2009},
	Ee = {http://dx.doi.org/10.1007/978-3-642-04138-9_8},
	Pages = {97-111},
	Title = {Algebraic Side-Channel Attacks on the AES: Why Time also Matters in DPA},
	Year = {2009}}

@proceedings{DBLP:conf/ches/2009,
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {CHES},
	Editor = {Christophe Clavier and Kris Gaj},
	Ee = {http://dx.doi.org/10.1007/978-3-642-04138-9},
	Isbn = {978-3-642-04137-2},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {Cryptographic Hardware and Embedded Systems - CHES 2009, 11th International Workshop, Lausanne, Switzerland, September 6-9, 2009, Proceedings},
	Volume = {5747},
	Year = {2009}}

@inproceedings{DBLP:conf/eurocrypt/FaugereP06,
	Author = {Jean-Charles Faug{\`e}re and Ludovic Perret},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {Advances in Cryptology -- EUROCRYPT 2006},
	Crossref = {DBLP:conf/eurocrypt/2006},
	Ee = {http://dx.doi.org/10.1007/11761679_3},
	Pages = {30-47},
	Title = {Polynomial Equivalence Problems: Algorithmic and Theoretical Aspects},
	Year = {2006}}

@proceedings{DBLP:conf/eurocrypt/2006,
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {Advances in Cryptology -- EUROCRYPT},
	Editor = {Serge Vaudenay},
	Isbn = {3-540-34546-9},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {Advances in Cryptology - EUROCRYPT 2006, 25th Annual International Conference on the Theory and Applications of Cryptographic Techniques, St. Petersburg, Russia, May 28 - June 1, 2006, Proceedings},
	Volume = {4004},
	Year = {2006}}

@inproceedings{DBLP:conf/eurocrypt/FaugereOPT10,
	Author = {Jean-Charles Faug{\`e}re and Ayoub Otmani and Ludovic Perret and Jean-Pierre Tillich},
	Booktitle = {Advances in Cryptology -- EUROCRYPT 2010},
	Ee = {http://dx.doi.org/10.1007/978-3-642-13190-5_14},
	Pages = {279-298},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Volume = {6110},
	Year = {2010},
	Yitle = {Algebraic Cryptanalysis of {McEliece} Variants with Compact Keys}}

@inproceedings{DBLP:conf/casc/Faugere09,
	Author = {Jean-Charles Faug{\`e}re},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {CASC},
	Crossref = {DBLP:conf/casc/2009},
	Ee = {http://dx.doi.org/10.1007/978-3-642-04103-7_7},
	Pages = {79-80},
	Title = {Solving Structured Polynomial Systems and Applications to Cryptology},
	Year = {2009}}

@proceedings{DBLP:conf/casc/2009,
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {CASC},
	Editor = {Vladimir P. Gerdt and Ernst W. Mayr and Evgenii V. Vorozhtsov},
	Ee = {http://dx.doi.org/10.1007/978-3-642-04103-7},
	Isbn = {978-3-642-04102-0},
	Publisher = {Springer Verla},
	Series = {Lecture Notes in Computer Science},
	Title = {Computer Algebra in Scientific Computing, 11th International Workshop, CASC 2009, Kobe, Japan, September 13-17, 2009. Proceedings},
	Volume = {5743},
	Year = {2009}}

@article{blum-kalai-wasserman:acm2003,
	Author = {Avrim Blum and Adam Kalai and Hal Wasserman},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Ee = {http://doi.acm.org/10.1145/792538.792543},
	Journal = {J. ACM},
	Number = {4},
	Pages = {506-519},
	Title = {Noise-tolerant learning, the parity problem, and the statistical query model},
	Volume = {50},
	Year = {2003}}

@inproceedings{DBLP:conf/stoc/Peikert09,
	Author = {Chris Peikert},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {Proceedings of the 41st Annual ACM Symposium on Theory of Computing, STOC 2009},
	Crossref = {DBLP:conf/stoc/2009},
	Ee = {http://doi.acm.org/10.1145/1536414.1536461},
	Pages = {333-342},
	Title = {Public-key cryptosystems from the worst-case shortest vector problem: extended abstract},
	Year = {2009}}

@proceedings{DBLP:conf/stoc/2009,
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {STOC},
	Editor = {Michael Mitzenmacher},
	Isbn = {978-1-60558-506-2},
	Publisher = {ACM},
	Title = {Proceedings of the 41st Annual ACM Symposium on Theory of Computing, STOC 2009},
	Year = {2009}}

@inproceedings{DBLP:conf/crypto/BlumFKL93,
	Author = {Avrim Blum and Merrick L. Furst and Michael J. Kearns and Richard J. Lipton},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {CRYPTO},
	Crossref = {DBLP:conf/crypto/1993},
	Ee = {http://dx.doi.org/10.1007/3-540-48329-2_24},
	Pages = {278-291},
	Title = {Cryptographic Primitives Based on Hard Learning Problems},
	Year = {1993}}

@proceedings{DBLP:conf/crypto/1993,
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {CRYPTO},
	Editor = {Douglas R. Stinson},
	Isbn = {3-540-57766-1},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {Advances in Cryptology - CRYPTO '93, 13th Annual International Cryptology Conference, Santa Barbara, California, USA, August 22-26, 1993, Proceedings},
	Volume = {773},
	Year = {1994}}

@inproceedings{DBLP:conf/focs/ImpagliazzoZ89,
	Author = {Russell Impagliazzo and David Zuckerman},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {FOCS},
	Crossref = {DBLP:conf/focs/FOCS30},
	Pages = {248-253},
	Title = {How to Recycle Random Bits},
	Year = {1989}}

@proceedings{DBLP:conf/focs/FOCS30,
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {FOCS},
	Publisher = {IEEE},
	Title = {30th Annual Symposium on Foundations of Computer Science, 30 October-1 November 1989, Research Triangle Park, North Carolina, USA},
	Year = {1989}}

@inproceedings{DBLP:conf/approx/Lyubashevsky05,
	Author = {Vadim Lyubashevsky},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {APPROX-RANDOM},
	Crossref = {DBLP:conf/approx/2005},
	Ee = {http://dx.doi.org/10.1007/11538462_32},
	Pages = {378-389},
	Title = {The Parity Problem in the Presence of Noise, Decoding Random Linear Codes, and the Subset Sum Problem},
	Year = {2005}}

@proceedings{DBLP:conf/approx/2005,
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {APPROX-RANDOM},
	Crossref = {DBLP:conf/approx/2005},
	Editor = {Chandra Chekuri and Klaus Jansen and Jos{\'e} D. P. Rolim and Luca Trevisan},
	Isbn = {3-540-28239-4},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {Approximation, Randomization and Combinatorial Optimization, Algorithms and Techniques, 8th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2005 and 9th InternationalWorkshop on Randomization and Computation, RANDOM 2005, Berkeley, CA, USA, August 22-24, 2005, Proceedings},
	Volume = {3624},
	Year = {2005}}

@inproceedings{DBLP:conf/stoc/Regev05,
	Author = {Oded Regev},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {STOC},
	Crossref = {DBLP:conf/stoc/2005},
	Ee = {http://doi.acm.org/10.1145/1060590.1060603},
	Pages = {84-93},
	Title = {On lattices, learning with errors, random linear codes, and cryptography},
	Year = {2005}}

@proceedings{DBLP:conf/stoc/2005,
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {STOC},
	Editor = {Harold N. Gabow and Ronald Fagin},
	Isbn = {1-58113-960-8},
	Publisher = {ACM},
	Title = {Proceedings of the 37th Annual ACM Symposium on Theory of Computing, Baltimore, MD, USA, May 22-24, 2005},
	Year = {2005}}

@inproceedings{DBLP:conf/coco/Regev10,
	Author = {Oded Regev},
	Booktitle = {25th Annual IEEE Conference on Computational Complexity, CCC 2010},
	Ee = {http://doi.ieeecomputersociety.org/10.1109/CCC.2010.26},
	Pages = {191-204},
	Publisher = {IEEE Computer Society},
	Title = {The Learning with Errors Problem (Invited Survey)},
	Year = {2010}}

@inproceedings{DBLP:conf/eurocrypt/BerbainGP06,
	Author = {C{\^o}me Berbain and Henri Gilbert and Jacques Patarin},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {Advances in Cryptology -- EUROCRYPT 2006},
	Crossref = {DBLP:conf/eurocrypt/2006},
	Ee = {http://dx.doi.org/10.1007/11761679_8},
	Pages = {109-128},
	Title = {QUAD: A Practical Stream Cipher with Provable Security},
	Year = {2006}}

@book{DBLP:books/fm/GareyJ79,
	Author = {M. R. Garey and David S. Johnson},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Isbn = {0-7167-1044-7},
	Publisher = {W. H. Freeman},
	Title = {Computers and Intractability: A Guide to the Theory of NP-Completeness},
	Year = {1979}}

@article{FGLM93,
	Author = {Jean-Charles Faug\`ere and Patrizia M. Gianni and Daniel Lazard and Teo Mora},
	Journal = {Journal of Symbolic Computation},
	Number = 4,
	Pages = {329--344},
	Title = {Efficient Computation of Zero-Dimensional {Gr\"obner} Bases by Change of Ordering},
	Volume = 16,
	Year = 1993}

@article{Fau99,
	Author = {Jean-Charles Faug\`ere},
	Journal = {Journal of Pure and Applied Algebra},
	Month = {June},
	Pages = {61--88},
	Title = {A new efficient algorithm for computing {Gr\"obner} bases ({F4})},
	Volume = 139,
	Year = 1999}

@inproceedings{Fau02,
	Author = {Jean-Charles Faug\`ere},
	Booktitle = {Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation ISSAC},
	Editor = {T. Mora},
	Month = {July},
	Note = {isbn: 1-58113-484-3},
	Pages = {75--83},
	Publisher = {ACM Press},
	Title = {A new efficient algorithm for computing {Gr\"obner} bases without reduction to zero ({F5})},
	Year = 2002}

@phdthesis{Bar04,
	Author = {Magali Bardet},
	School = {Universit\'e de Paris VI},
	Title = {\'Etude des syst\`emes alg\'ebriques surd\'etermin\'es. Applications aux codes correcteurs et \`a la cryptographie},
	Year = 2004}

@inproceedings{BFS04,
	Author = {Magali Bardet and Jean-Charles Faug\`ere and Bruno Salvy},
	Booktitle = {Proc. International Conference on Polynomial System Solving (ICPSS)},
	Pages = {71--75},
	Title = {On the complexity of {G}r\"obner basis computation of semi-regular overdetermined algebraic equations},
	Year = 2004}

@techreport{BFS02,
	Author = {Magali Bardet and Jean-Charles Faug\`ere and Bruno Salvy},
	Institution = {INRIA},
	Note = {\url{http://www.inria.fr/rrrt/rr-5049.html}},
	Title = {Complexity study of {G}r\"obner basis computation},
	Year = 2002}

@inproceedings{BFSY05,
	Author = {Magali Bardet and Jean-Charles Faug\`ere and Bruno Salvy and Bo-Yin Yang},
	Booktitle = {Proc. of MEGA 2005, Eighth International Symposium on Effective Methods in Algebraic Geometry},
	Title = {Asymptotic Behaviour of the Degree of Regularity of Semi-Regular Polynomial Systems},
	Year = 2005}

@phdthesis{Buc65,
	Author = {Bruno Buchberger},
	School = {University of Innsbruck},
	Title = {Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal},
	Year = 1965}

@article{BCLA82,
	Author = {Bruno Buchberger and Georges E. Collins and Rudiger G. K. Loos and Rudolph Albrecht},
	Journal = {SIGSAM Bull.},
	Number = {4},
	Pages = {5--5},
	Publisher = {ACM},
	Title = {Computer algebra symbolic and algebraic computation},
	Volume = {16},
	Year = {1982}}

@article{DBLP:journals/siamcomp/Semaev09,
	Author = {Igor Semaev},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Ee = {http://dx.doi.org/10.1137/070700371},
	Journal = {SIAM J. Comput.},
	Number = {2},
	Pages = {388-409},
	Title = {Sparse Algebraic Equations over Finite Fields},
	Volume = {39},
	Year = {2009}}

@article{DBLP:journals/dcc/RaddumS08,
	Author = {H{\aa}vard Raddum and Igor Semaev},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Ee = {http://dx.doi.org/10.1007/s10623-008-9180-z},
	Journal = {Des. Codes Cryptography},
	Number = {1-3},
	Pages = {147-160},
	Title = {Solving Multiple Right Hand Sides linear equations},
	Volume = {49},
	Year = {2008}}

@article{DBLP:journals/dcc/Semaev08,
	Author = {Igor Semaev},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Ee = {http://dx.doi.org/10.1007/s10623-008-9182-x},
	Journal = {Des. Codes Cryptography},
	Number = {1-3},
	Pages = {47-60},
	Title = {On solving sparse algebraic equations over finite fields},
	Volume = {49},
	Year = {2008}}

@article{DBLP:journals/jsc/BrickensteinD09,
	Author = {Michael Brickenstein and Alexander Dreyer},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Ee = {http://dx.doi.org/10.1016/j.jsc.2008.02.017},
	Journal = {J. Symb. Comput.},
	Number = {9},
	Pages = {1326-1345},
	Title = {PolyBoRi: A framework for Gr{\"o}bner-basis computations with Boolean polynomials},
	Volume = {44},
	Year = {2009}}

@inproceedings{DBLP:conf/ima/CourtoisB07,
	Author = {Nicolas Courtois and Gregory V. Bard},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {IMA Int. Conf.},
	Crossref = {DBLP:conf/ima/2007},
	Ee = {http://dx.doi.org/10.1007/978-3-540-77272-9_10},
	Pages = {152-169},
	Title = {Algebraic Cryptanalysis of the Data Encryption Standard},
	Year = {2007}}

@proceedings{DBLP:conf/ima/2007,
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {IMA Int. Conf.},
	Editor = {Steven D. Galbraith},
	Isbn = {978-3-540-77271-2},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {Cryptography and Coding, 11th IMA International Conference, Cirencester, UK, December 18-20, 2007, Proceedings},
	Volume = {4887},
	Year = {2007}}

@inproceedings{DBLP:conf/asiacrypt/StehleSTX09,
	Author = {Damien Stehl{\'e} and Ron Steinfeld and Keisuke Tanaka and Keita Xagawa},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {ASIACRYPT},
	Crossref = {DBLP:conf/asiacrypt/2009},
	Ee = {http://dx.doi.org/10.1007/978-3-642-10366-7_36},
	Pages = {617-635},
	Title = {Efficient Public Key Encryption Based on Ideal Lattices},
	Year = {2009}}

@proceedings{DBLP:conf/asiacrypt/2009,
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {ASIACRYPT},
	Editor = {Mitsuru Matsui},
	Ee = {http://dx.doi.org/10.1007/978-3-642-10366-7},
	Isbn = {978-3-642-10365-0},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {Advances in Cryptology - ASIACRYPT 2009, 15th International Conference on the Theory and Application of Cryptology and Information Security, Tokyo, Japan, December 6-10, 2009. Proceedings},
	Volume = {5912},
	Year = {2009}}

@inproceedings{DBLP:conf/eurocrypt/LyubashevskyPR10,
	Author = {Vadim Lyubashevsky and Chris Peikert and Oded Regev},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {Advances in Cryptology -- EUROCRYPT 2010},
	Pages = {1-23},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {On Ideal Lattices and Learning with Errors over Rings},
	Volume = {6110},
	Year = {2010}}

@article{DBLP:journals/corr/abs-1001-2140,
	Author = {Mukundan Madhavan and Andrew Thangaraj and Yogesh Sankarasubramaniam and Kapali Viswanathan},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Ee = {http://arxiv.org/abs/1001.2140},
	Journal = {CoRR},
	Title = {NLHB : A Non-Linear Hopper Blum Protocol},
	Volume = {abs/1001.2140},
	Year = {2010}}

@inproceedings{DBLP:conf/eurocrypt/FouqueGS05,
	Author = {Pierre-Alain Fouque and Louis Granboulan and Jacques Stern},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {Advances in Cryptology -- EUROCRYPT 2005},
	Crossref = {DBLP:conf/eurocrypt/2005},
	Pages = {341-353},
	Title = {Differential Cryptanalysis for Multivariate Schemes},
	Year = {2005}}

@inproceedings{FL06,
	Author = {Pierre-Alain Fouque and {\'E}ric Levieil},
	Booktitle = {Security and Cryptography for Networks, 5th International Conference, SCN 2006},
	Editor = {Roberto De Prisco and Moti Yung},
	Pages = {348-359},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {An Improved {LPN} Algorithm},
	Volume = {4116},
	Year = {2006}}

@inproceedings{WHLCY05,
	Author = {Lih-Chung Wang and Yuh-Hua Hu, Feipei Lai and Chun-Yen Chou and Bo-Yin Yang},
	Booktitle = {PKC 05},
	Title = {{Tractable Rational Map Signature}},
	Year = 2005}

@misc{DY07,
	Author = {Jintai Ding and Bo-Yin Yang},
	Howpublished = {Cryptology ePrint Archive, Report 2007/137},
	Title = {Multivariates Polynomials for Hashing},
	Year = 2007}

@article{FGLM93,
	Author = {Jean-Charles Faug\`ere and Patrizia M. Gianni and Daniel Lazard and Teo Mora},
	Journal = {Journal of Symbolic Computation},
	Number = 4,
	Pages = {329--344},
	Title = {Efficient Computation of Zero-Dimensional {Gr\"obner} Bases by Change of Ordering},
	Volume = 16,
	Year = 1993}

@inproceedings{FJ03,
	Author = {Jean-Charles Faug\`ere and Antoine Joux},
	Booktitle = {Advances in Cryptology - CRYPTO 2003},
	Editor = {Dan Boneh},
	Pages = {44--60},
	Publisher = {Springer Verlag},
	Series = {LNCS},
	Title = {Algebraic cryptanalysis of {Hidden Field Equation (HFE)} cryptosystems using {Gr\"obner} bases},
	Volume = 2729,
	Year = 2003}

@inproceedings{GJS06,
	Author = {Louis Granboulan and Antoine Joux and Jacques Stern},
	Bibsource = {IACR, http://www.iacr.org},
	Booktitle = {CRYPTO},
	Pages = {345-356},
	Title = {Inverting HFE Is Quasipolynomial},
	Year = {2006}}

@misc{Magma,
	Author = {MAGMA},
	Note = {http://magma.maths.usyd.edu.au},
	Title = {High performance software for Algebra, Nuber Theory, and Geometry --- a large commercial software package}}

@inproceedings{BFP08a,
	Author = {Luk Bettale and Jean-Charles Faug\`ere and Ludovic Perret},
	Booktitle = {Progress in Cryptology -- AFRICACRYPT 2008},
	Pages = {143--155},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {Cryptanalysis of the {TRMS} Signature Scheme of {PKC'05}},
	Volume = 5023,
	Year = 2008}

@inproceedings{FP08,
	Author = {Jean-Charles Faug\`ere and Ludovic Perret},
	Booktitle = {SCC 08},
	Title = {On the security of UOV},
	Year = 2008}

@inproceedings{BFP08b,
	Author = {Luk Bettale and Jean-Charles Faug\`ere and Ludovic Perret},
	Booktitle = {Information Security and Cryptology -- INSCRYPT 2008},
	Note = {to appear},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {Security analysis of multivariate polynomials for hashing},
	Year = 2008}

@inproceedings{HFEIP,
	Author = {Jacques Patarin},
	Booktitle = {Advances in Cryptology -- EUROCRYPT 1996},
	Pages = {33--48},
	Publisher = {Springer--Verlag},
	Series = {LNCS},
	Title = {{Hidden Fields Equations (HFE)} and {Isomorphisms of Polynomials (IP)}: two new families of asymmetric algorithms},
	Volume = 1070,
	Year = 1996}

@inproceedings{C*,
	Author = {Tsutomu Matsumoto and Hideki Imai},
	Booktitle = {Advances in Cryptology -- EUROCRYPT 1988},
	Pages = {419--453},
	Publisher = {Springer--Verlag},
	Series = {LNCS},
	Title = {Public Quadratic Polynomial-tuples for Efficient Signature-Verification and Message-Encryption},
	Volume = 330,
	Year = 1988}

@book{AL94,
	Author = {William W. Adams and Philippe Loustaunau},
	Publisher = {AMS},
	Series = {Graduate Studies in Mahematics},
	Title = {An Introduction to Gr\"obner Bases},
	Volume = 3,
	Year = 1994}

@book{CLO05,
	Author = {David A. Cox and John B. Little and Don O'Shea},
	Publisher = {Springer Verlag},
	Title = {Ideals, Varieties and Algorithms},
	Year = 2005}

@inproceedings{AM07,
	Author = {Jean-Philippe Aumasson and Willi Meier},
	Booktitle = {Information Security and Cryptology - ICISC 2007},
	Note = {isbn: 978-3-540-76787-9},
	Pages = {309--323},
	Publisher = {Springer Verlag},
	Series = {LNCS},
	Title = {Analysis of Multivariate Hash Functions},
	Volume = 4817,
	Year = 2007}

@inproceedings{BRP07,
	Author = {Olivier Billet and Matthew J. B. Robshaw and Thomas Peyrin},
	Booktitle = {ACISP},
	Pages = {82--95},
	Publisher = {Springer Verlag},
	Series = {LNCS},
	Title = {On building hash functions from multivariate quadratic equations},
	Volume = 4586,
	Year = 2007}

@misc{WFLY04,
	Author = {Xiaoyun Wang and Dengguo Feng and Xuejia Lai and Hongbo Yu},
	Howpublished = {Cryptology ePrint Archive, Report 2004/199},
	Title = {Collisions for Hash Functions {MD4}, {MD5}, {HAVAL}-128 and {RIPEMD}},
	Year = 2004}

@inproceedings{WLF+05,
	Author = {Xiaoyun Wang and Xuejia Lai and Dengguo Feng and Hui Chen and Xiuyuan Yu},
	Booktitle = {Advances in Cryptology -- EUROCRYPT 2005},
	Editor = {Ronald Cramer},
	Pages = {1--18},
	Publisher = {Springer Verlag},
	Series = {LNCS},
	Title = {Cryptanalysis of the Hash Functions {MD4} and {RIPEMD}},
	Volume = 3494,
	Year = 2005}

@inproceedings{WYY05b,
	Author = {Xiaoyun Wang and Hongbo Yu and Yiqun Lisa Yin},
	Booktitle = {CRYPTO},
	Editor = {Victor Shoup},
	Pages = {1--16},
	Publisher = {Springer Verlag},
	Series = {LNCS},
	Title = {Efficient Collision Search Attacks on {SHA-0}},
	Volume = 3621,
	Year = 2005}

@inproceedings{WYY05a,
	Author = {Xiaoyun Wang and Yiqun Lisa Yin and Hongbo Yu},
	Booktitle = {CRYPTO},
	Editor = {Victor Shoup},
	Pages = {17--36},
	Publisher = {Springer Verlag},
	Series = {LNCS},
	Title = {Finding Collisions in the Full {SHA-1}},
	Volume = 3621,
	Year = 2005}

@misc{LL08,
	Author = {Yiyuan Luo and Xuejia Lai},
	Howpublished = {Cryptology ePrint Archive, Report 2008/350},
	Note = {\url{http://eprint.iacr.org/}},
	Title = {Higher Order Differential Cryptanalysis of Multivariate Hash Functions},
	Year = {2008}}

@misc{FIPS180-1,
	Author = {National Institute of Standards and Technology (NIST)},
	Note = {\url{http://www.itl.nist.gov/fipspubs/fip180-1.htm}},
	Title = {{Federal Information Processing Standards Publication (FIPS)} 180-1},
	Year = 1995}

@inproceedings{CR06,
	Author = {Christophe De Canni{\`e}re and Christian Rechberger},
	Booktitle = {ASIACRYPT},
	Pages = {1-20},
	Publisher = {Springer Verlag},
	Series = {LNCS},
	Title = {Finding {SHA-1} Characteristics: General Results and Applications},
	Volume = 4284,
	Year = 2006}

@misc{WYY05,
	Author = {Xiaoyun Wang and Andrew Yao and Frances Yao},
	Howpublished = {CRPTYO 2005 Rump Session},
	Title = {New collision search for {SHA-1}},
	Year = 2005}

@inproceedings{BERW,
	Author = {Andrey Bogdanov and Thomas Eisenbarth and Andy Rupp and Christopher Wolf},
	Booktitle = {CHES '08: Proceeding sof the 10th international workshop on Cryptographic Hardware and Embedded Systems},
	Location = {Washington, DC, USA},
	Pages = {45--61},
	Publisher = {Springer-Verlag},
	Title = {Time-Area Optimized Public-Key Engines: $\mathcal{MQ}$-Cryptosystems as Replacement for Elliptic Curves?},
	Year = {2008}}

@article{Sza01,
	Author = {Agnes Szanto},
	Journal = {Journal of Pure and Applied Algebra},
	Title = {Multivariate subresultants using {Jouanolou's} resultant matrices},
	Year = 2001}

@inproceedings{Laz83,
	Author = {Daniel Lazard},
	Booktitle = {EUROCAL},
	Pages = {146-156},
	Title = {Gr{\"o}bner-Bases, Gaussian elimination and resolution of systems of algebraic equations},
	Year = {1983}}

@inproceedings{Giu84,
	Author = {Marc Giusti},
	Booktitle = {EUROSAM},
	Number = {Computation},
	Pages = {159-171},
	Title = {Some Effectivity Problems in Polynomial Ideal Theory},
	Year = {1984}}

@inproceedings{AFI+,
	Author = {Gw\'enol\'e Ars and Jean-Charles Faug\`ere and Hideki Imai and Mitsuru Kawazoe and Makoto Sugita},
	Booktitle = {ASIACRYPT 2004},
	Editor = {Pil Joong Lee},
	Month = {December},
	Pages = {338--353},
	Publisher = {Springer Verlag},
	Series = {LNCS},
	Title = {Comparison between {XL} and {Gr\"obner} basis algorithms},
	Volume = 3329,
	Year = 2004}

@inproceedings{CKPS,
	Author = {Nicolas Courtois and Alexander Klimov and Jacques Patarin and Adi Shamir},
	Booktitle = {Advances in Cryptology - EUROCRYPT 2000},
	Pages = {392--407},
	Publisher = {Springer Verlag},
	Series = {LNCS},
	Title = {Efficient algorithms for solving overdefined systems of multivariate polynomial equations},
	Volume = 1807,
	Year = 2000}

@inproceedings{YCC04,
	Author = {Bo-Yin Yang and Jiun-Ming Chen and Nicolas Courtois},
	Booktitle = {ICICS 2004},
	Pages = {401-413},
	Title = {On Asymptotic Security Estimates in XL and {Gr\"obner} Bases-Related Algebraic Cryptanalysis},
	Year = 2004}

@inproceedings{BWP05,
	Author = {An Braeken and Christopher Wolf and Bart Preneel},
	Booktitle = {Topics in Cryptology - CT-RSA 2005},
	Month = {February},
	Pages = {29-43},
	Publisher = {Springer Verlag},
	Series = {LNCS},
	Title = {A Study of the Security of {Unbalanced Oil and Vinegar} Signature Schemes},
	Volume = 3376,
	Year = 2005}

@misc{OV,
	Author = {Jacques Patarin},
	Howpublished = {presented at the Dagstuhl Workshop on Cryptography},
	Title = {The {Oil} and {Vinegar} Signature Scheme},
	Year = 1997}

@inproceedings{SFLASH,
	Author = {Jacques Patarin and Louis Goubin and Nicolas Courtois},
	Booktitle = {Advances in Cryptology - Asiacrypt'98},
	Pages = {35-49},
	Publisher = {Springer Verlag},
	Title = {C$^*-+$ and HM: Variations Around Two Schemes of T.Matsumoto and H.Imai},
	Volume = 1514,
	Year = 1998}

@inproceedings{QUARTZ,
	Author = {Jacques Patarin and Nicolas Courtois and Louis Goubin},
	Booktitle = {CT-RSA'01},
	Pages = {282-297},
	Publisher = {Springer Verlag},
	Title = {QUARTZ, 128-Bit Long Digital Signatures},
	Volume = 2020,
	Year = 2001}

@misc{WPTAX,
	Author = {Christopher Wolf and Bart Preneel},
	Howpublished = {{Cryptology ePrint Archive, Report 2005/077}},
	Note = {\url{http://eprint.iacr.org/}},
	Title = {{Taxonomy of Public Key Schemes based on the problem of Multivariate Quadratic equations}},
	Year = 2005}

@inproceedings{DFSS07,
	Author = {Vivien Dubois and Pierre-Alain Fouque and Adi Shamir and Jacques Stern},
	Booktitle = {Advances in Cryptology - CRYPTO'07},
	Pages = {1-12},
	Publisher = {Springer Verlag},
	Title = {Practical Cryptanalysis of SFLASH},
	Volume = 4622,
	Year = 2007}

@book{GJ79,
	Author = {Michael R. Garey and David S. Johnson},
	Publisher = {W. H. Freeman},
	Title = {Computers and Intractability: A Guide to the Theory of NP-Completeness},
	Year = 1979}

@inproceedings{HMo,
	Author = {Jacques Patarin and Nicolas Courtois and Louis Goubin},
	Booktitle = {Advances in Cryptology - ASIACRYPT'98},
	Pages = {35-50},
	Publisher = {Springer Verlag},
	Title = {${C}_{-+}^*$ and ${HM}$: {V}ariations on {T}wo {S}chemes of {T}.{M}atsumoto and {H}.{I}mai},
	Volume = 1514,
	Year = 1998}

@misc{HMext,
	Author = {Jacques Patarin and Nicolas Courtois and Louis Goubin},
	Howpublished = {{Available From the Authors}},
	Title = {${C}_{-+}^*$ and ${HM}$: {V}ariations on {T}wo {S}chemes of {T}.{M}atsumoto and {H}.{I}mai, {E}xtended {V}ersion},
	Year = 1998}

@book{FF,
	Author = {Rudolf Liddl and Harald Niederreiter},
	Publisher = {Longman Higher Education},
	Title = {Introduction to Finite Fields},
	Year = {1983}}

@inproceedings{[C],
	Author = {Hideki Imai and Tsutomu Matsumoto},
	Booktitle = {Algebraic Algorithms and Error Correcting Codes (AAECC-3)},
	Pages = {108-119},
	Publisher = {Lecture Notes in Computer Science},
	Title = {{Algebraic Methods for Constructing Asymmetric Cryptosystems}},
	Volume = 229,
	Year = 1985}

@inproceedings{BERW,
	Author = {Andrey Bogdanov and Thomas Eisenbarth and Andy Rupp and Christopher Wolf},
	Booktitle = {Cryptographic Hardware and Embedded Systems (CHES)},
	Pages = {145-61},
	Publisher = {Lecture Notes in Computer Science},
	Title = {{Time-Area Optimized Public-Key Engines: MQ -Cryptosystems as Replacement for Elliptic Curves?}},
	Volume = 5154,
	Year = 2008}

@article{Attaqued1,
	Author = {Vivien Dubois and Pierre-Alain Fouque and Adi Shamir and Jacques Stern},
	Journal = {Advances in Cryptology - CRYPTO'07},
	Pages = {1-12},
	Publisher = {Springer Verlag},
	Title = {Practical Cryptanalysis of SFLASH},
	Volume = 4622,
	Year = 2007}

@article{Cryptanalyse_C_star,
	Author = {Jacques Patarin},
	Journal = {Advances in Cryptology - CRYPTO'95},
	Pages = {248-261},
	Publisher = {Springer Verlag},
	Title = {Cryptanalysis of the Matsumoto and Imai Public Key Scheme of Eurocrypt'88},
	Volume = {963},
	Year = {1995}}

@article{OVShamir,
	Author = {Aviad Kipnis and Adi Shamir},
	Journal = {CRYPTO 98},
	Pages = {257-266},
	Publisher = {Springer Verlag},
	Title = {Cryptanalysis of the Oil and Vinegar Signature Scheme},
	Volume = {1462},
	Year = 1998}

@article{WDGY,
	Author = {Zhiping Wu, Jintai Ding, Jason E. Gower, Dingfeng Ye},
	Journal = {ICCSA},
	Pages = {595-602},
	Publisher = {Springer Verlag},
	Title = {Perturbed Hidden Matrix Cryptosystems},
	Volume = {1462},
	Year = 2005}

@inproceedings{DBLP:conf/pkc/Ding04,
	Author = {Jintai Ding},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {Public Key Cryptography},
	Crossref = {DBLP:conf/pkc/2004},
	Pages = {305-318},
	Title = {A New Variant of the Matsumoto-Imai Cryptosystem through Perturbation},
	Year = {2004}}

@inproceedings{DBLP:conf/stoc/AjtaiD97,
	Author = {Mikl{\'o}s Ajtai and Cynthia Dwork},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {STOC},
	Pages = {284-293},
	Title = {A Public-Key Cryptosystem with Worst-Case/Average-Case Equivalence},
	Year = {1997}}

@inproceedings{DBLP:conf/crypto/GoldreichGH97,
	Author = {Oded Goldreich and Shafi Goldwasser and Shai Halevi},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {CRYPTO},
	Crossref = {DBLP:conf/crypto/1997},
	Ee = {http://dx.doi.org/10.1007/BFb0052230},
	Pages = {105-111},
	Title = {Eliminating Decryption Errors in the Ajtai-Dwork Cryptosystem},
	Year = {1997}}

@inproceedings{DBLP:conf/stoc/Regev03,
	Author = {Oded Regev},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {STOC},
	Crossref = {DBLP:conf/stoc/2003},
	Ee = {http://doi.acm.org/10.1145/780542.780603},
	Pages = {407-416},
	Title = {New lattice based cryptographic constructions},
	Year = {2003}}

@inproceedings{DBLP:conf/stoc/Ajtai96,
	Author = {Mikl{\'o}s Ajtai},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {STOC},
	Ee = {http://doi.acm.org/10.1145/237814.237838},
	Pages = {99-108},
	Title = {Generating Hard Instances of Lattice Problems (Extended Abstract)},
	Year = {1996}}

@inproceedings{GPV08,
	Author = {Craig Gentry and Chris Peikert and Vinod Vaikuntanathan},
	Booktitle = {STOC 08: Proceedings of the 40th annual ACM symposium on Theory of computing},
	Owner = {malb},
	Pages = {197--206},
	Publisher = {ACM},
	Timestamp = {2009.08.12},
	Title = {Trapdoors for hard lattices and new cryptographic constructions},
	Year = {2008}}

@phdthesis{Gentry09:phd,
	Author = {Craig Gentry},
	Note = {Available at \url{http://crypto.stanford.edu/craig}},
	School = {Stanford University},
	Title = {A fully homomorphic encryption scheme},
	Year = {2009}}

@inproceedings{brakerski-vaikuntanathan:focs2011,
	Author = {Zvika Brakerski and Vinod Vaikuntanathan},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011},
	Editor = {Rafail Ostrovsky},
	Ee = {http://dx.doi.org/10.1109/FOCS.2011.12},
	Pages = {97-106},
	Publisher = {IEEE},
	Title = {Efficient Fully Homomorphic Encryption from (Standard) {LWE}},
	Year = {2011}}

@inproceedings{albrecht-farshim-faugere-perret:asiacrypt2011,
	Address = {Berlin, Heidelberg, New York},
	Author = {Martin R.~Albrecht and Pooya Farshim and Jean-Charles Faug{\`e}re and Ludovic Perret},
	Booktitle = {Advances in Cryptology -- ASIACRYPT 2011},
	Note = {full version available as Cryptology ePrint Archive, Report 2011/289, 2011 \url{http://eprint.iacr.org/}},
	Pages = {179--196},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {Polly {C}racker, Revisited},
	Volume = 7073,
	Year = 2011}

@misc{graycode,
	Author = {Frank Gray},
	Month = {March},
	Note = {US Patent No. 2,632,058},
	Owner = {malb},
	Timestamp = {2008.09.15},
	Title = {Pulse code communication},
	Year = {1953}}

@inproceedings{chen-nguyen:asiacrypt2011,
	Acmid = {2184024},
	Address = {Berlin, Heidelberg},
	Author = {Chen, Yuanmi and Nguyen, Phong Q.},
	Booktitle = {Advances in Cryptology - ASIACRYPT 2011},
	Doi = {10.1007/978-3-642-25385-0_1},
	Isbn = {978-3-642-25384-3},
	Location = {Seoul, South Korea},
	Numpages = {20},
	Pages = {1--20},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {{BKZ} 2.0: better lattice security estimates},
	Url = {http://dx.doi.org/10.1007/978-3-642-25385-0_1},
	Volume = 7073,
	Year = {2011},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-642-25385-0_1}}

@article{rueckert-schneider:eprint2010,
	Author = {Markus R{\"u}ckert and Michael Schneider},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Ee = {http://eprint.iacr.org/2010/137},
	Journal = {IACR Cryptology ePrint Archive},
	Pages = {137},
	Title = {Estimating the Security of Lattice-based Cryptosystems},
	Volume = {2010},
	Year = {2010}}

@incollection{micciancio-regev:pqc2009,
	__Markedentry = {[malb:6]},
	Address = {Berlin, Heidelberg, New York},
	Author = {Daniele Micciancio and Oded Regev},
	Booktitle = {Post-Quantum Cryptography},
	Editor = {Bernstein, Daniel J. and Buchmann, Johannes and Dahmen, Erik},
	Owner = {malb},
	Pages = {147-191},
	Publisher = {Springer Verlag},
	Timestamp = {2011.11.09},
	Title = {Lattice-based Cryptography},
	Year = {2009}}

@misc{kirchner:eprint2011,
	Author = {Paul Kirchner},
	Howpublished = {Cryptology ePrint Archive, Report 2011/377},
	Note = {\url{http://eprint.iacr.org/}},
	Title = {Improved Generalized Birthday Attack},
	Year = 2011}

@inproceedings{applebaum-cash-peikert-sahai:crypto2009,
	Address = {Berlin, Heidelberg, New York},
	Author = {Applebaum, Benny and Cash, David and Peikert, Chris and Sahai, Amit},
	Booktitle = {Advances in Cryptology -- CRYPTO 2009},
	Doi = {10.1007/978-3-642-03356-8_35},
	Numpages = 24,
	Pages = {595-618},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {Fast Cryptographic Primitives and Circular-Secure Encryption Based on Hard Learning Problems},
	Year = 2009,
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-642-03356-8_35}}

@inproceedings{gentry-halevi-smart:crypto2012,
	address = {Berlin, Heidelberg, New York},
    title = {Homomorphic Evaluation of the {AES} Circuit},
	author = {Craig Gentry and Shai Halevi and Nigel P. Smart},
	editor = {Reihaneh Safavi-Naini and Ran Canetti},
	pages = {850-867},
	publisher = {Springer Verlag},
	series = {Lecture Notes in Computer Science},
	booktitle = {Advances in Cryptology -- CRYPTO 2012},
	volume = {7417},
	year = {2012}}

@inproceedings{ajtai-kumar-sivakumar:ccc2002,
	Author = {Mikl{\'o}s Ajtai and Ravi Kumar and D. Sivakumar},
	Booktitle = {IEEE Conference on Computational Complexity},
	Ee = {http://computer.org/proceedings/ccc/1468/14680053abs.htm},
	Pages = {53-57},
	Title = {Sampling Short Lattice Vectors and the Closest Lattice Vector Problem},
	Year = {2002}}

@manual{mpmath,
	Author = {Fredrik Johansson and others},
	Key = {mpmath},
	Month = {February},
	Note = {{\tt http://code.google.com/p/mpmath/}},
	Title = {mpmath: a {P}ython library for arbitrary-precision floating-point arithmetic (version 0.17)},
	Year = {2011}}

@article{jeannerod-pernet-storjohann:cup2012,
	Author = {Claude-Pierre Jeannerod and Cl{\'e}ment Pernet and Arne Storjohann},
	Journal = {{\tt arXiv:1112.5717}},
	Pages = {35 pages},
	Title = {Rank-profile revealing {G}aussian elimination and the {CUP} matrix decomposition},
	Year = {2012}}

@article{LindnerP10,
	Author = {Richard Lindner and Chris Peikert},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Date-Modified = {2012-09-07 12:05:58 +0200},
	Ee = {http://eprint.iacr.org/2010/592},
	Journal = {IACR Cryptology ePrint Archive},
	Pages = {592},
	Title = {Better Key Sizes (and Attacks) for {LWE}-Based Encryption},
	Volume = {2010},
	Year = {2010}}

@inproceedings{DBLP:conf/codcry/HanrotPS11,
	Author = {Guillaume Hanrot and Xavier Pujol and Damien Stehl{\'e}},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {IWCC},
	Crossref = {DBLP:conf/codcry/2011},
	Ee = {http://dx.doi.org/10.1007/978-3-642-20901-7_10},
	Pages = {159-190},
	Title = {Algorithms for the Shortest and Closest Lattice Vector Problems},
	Year = {2011}}

@proceedings{DBLP:conf/codcry/2011,
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {IWCC},
	Editor = {Yeow Meng Chee and Zhenbo Guo and San Ling and Fengjing Shao and Yuansheng Tang and Huaxiong Wang and Chaoping Xing},
	Ee = {http://dx.doi.org/10.1007/978-3-642-20901-7},
	Isbn = {978-3-642-20900-0},
	Publisher = {Springer},
	Series = {Lecture Notes in Computer Science},
	Title = {Coding and Cryptology - Third International Workshop, IWCC 2011, Qingdao, China, May 30-June 3, 2011. Proceedings},
	Volume = {6639},
	Year = {2011}}

@inproceedings{DBLP:conf/icits/BaigneresV08,
	Author = {Thomas Baign{\`e}res and Serge Vaudenay},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {ICITS},
	Crossref = {DBLP:conf/icits/2008},
	Ee = {http://dx.doi.org/10.1007/978-3-540-85093-9_20},
	Pages = {210-222},
	Title = {The Complexity of Distinguishing Distributions (Invited Talk)},
	Year = {2008}}

@proceedings{DBLP:conf/icits/2008,
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {ICITS},
	Editor = {Reihaneh Safavi-Naini},
	Isbn = {978-3-540-85092-2},
	Publisher = {Springer},
	Series = {Lecture Notes in Computer Science},
	Title = {Information Theoretic Security, Third International Conference, ICITS 2008, Calgary, Canada, August 10-13, 2008, Proceedings},
	Volume = {5155},
	Year = {2008}}

@incollection{huang-liu-yang:pkc2012,
	Author = {Huang, Yun-Ju and Liu, Feng-Hao and Yang, Bo-Yin},
	Booktitle = {Public Key Cryptography -- PKC 2012},
	Date-Modified = {2013-02-10 21:27:23 +0000},
	Editor = {Fischlin, Marc and Buchmann, Johannes and Manulis, Mark},
	Pages = {190-205},
	Publisher = {Springer Verlag},
	Series = {Lecture Notes in Computer Science},
	Title = {Public-Key Cryptography from New Multivariate Quadratic Assumptions},
	Url = {http://dx.doi.org/10.1007/978-3-642-30057-8_12},
	Volume = {7293},
	Year = {2012},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-642-30057-8_12}}

@article{siegel1992toward,
	Author = {Siegel, A.},
	Publisher = {Citeseer},
	Title = {Toward a usable theory of chernoff bounds for heterogeneous and partially dependent random variables},
	Year = {1992}}

@misc{agrawal-gentry-halevi-sahai:eprint2012,
	Author = {Shweta Agrawal and Craig Gentry and Shai Halevi and Amit Sahai},
	Howpublished = {Cryptology ePrint Archive, Report 2012/714},
	Note = {\url{http://eprint.iacr.org/}},
	Title = {Sampling Discrete {G}aussians Efficiently and Obliviously},
	Year = {2012}}

@inproceedings{liu-nguyen:ctrsa2013,
  author    = {Mingjie Liu and
               Phong Q. Nguyen},
  title     = {Solving {BDD} by Enumeration: An Update},
  year      = {2013},
  pages     = {293-309},
  ee        = {http://dx.doi.org/10.1007/978-3-642-36095-4_19},
  editor    = {Ed Dawson},
  booktitle = {Topics in Cryptology - CT-RSA 2013},
  publisher = {Springer Verlag},
  series    = {Lecture Notes in Computer Science},
  volume    = {7779},
}

@manual{sagemath,
  title = {{S}age {M}athematics {S}oftware ({V}ersion 5.9)},
  author = {W.\thinspace{}A. Stein and others},
  organization = {The Sage Development Team},
  year = {2013},
  note = {{\tt http://www.sagemath.org}},
  key = {Sage}
}


@article{cohn2003new,
  title={New upper bounds on sphere packings I},
  author={Cohn, Henry and Elkies, Noam},
  journal={Annals of Mathematics},
  pages={689--714},
  year={2003},
  publisher={JSTOR}
}

@misc{albrecht-fitzpatrick-cabracas-goepfert-schneider:bitbucket2013,
  author = {Martin R.~Albrecht and Robert Fitzpatrick and  Daniel Cabracas and Florian Göpfert and Michael Schneider},
  title = {A Generator for {LWE} and {Ring-LWE} Instances},
  year = 2013,
  note = {available at \url{http://www.iacr.org/news/files/2013-04-29lwe-generator.pdf}}
}

@misc{scipy,
  author =    {Eric Jones and Travis Oliphant and Pearu Peterson and others},
  title =     {{SciPy}: Open source scientific tools for {Python}},
  year =      {2001--},
  url = "http://www.scipy.org/"
}

@manual{minpack,
    author = {Mor\'{e}, J. J. and Garbow, B. S. and Hillstrom, K. E.},
    journal = {ANL-80-74, Argonne National Laboratory},
    title = {{User Guide for MINPACK-1}},
    url = {http://www.mcs.anl.gov/\~{}more/ANL8074a.pdf},
    year = {1980}
}

@manual{helib,
  title = {Design and Implementation of a Homomorphic-Encryption Library},
  author = {Shai Halevi and Victor Shoup},
  year = 2013,
  url = {https://github.com/shaih/HElib},
}

@misc{utah-data-centre,
 author = {Kashmir Hill},
 title = {Blueprints Of {NSA}'s Ridiculously Expensive Data Center In {Utah} Suggest It Holds Less Info Than Thought},
 howpublished = {\url{http://www.forbes.com/sites/kashmirhill/2013/07/24/blueprints-of-nsa-data-center-in-utah-suggest-its-storage-capacity-is-less-impressive-than-thought/}},
 year = 2013,
}